Comment on “Isolating Polaritonic 2D-IR Transmission Spectra”

This Viewpoint responds to the analysis of 2D IR spectra of vibration cavity polaritons in the study reported in The Journal of Physical Chemistry Letters (Duan et al. 2021, 12, 11406). That report analyzed 2D IR spectra of strongly coupled molecules, such as W(CO)6 and nitroprusside anion, based on subtracting a background signal generated by polariton filtered free space signals. They assigned the resulting response as being due to excited polaritons. We point out in this Viewpoint that virtually all of the response can be properly reproduced using the physics of transmission through an etalon containing a material modeled with a complex dielectric function describing the ground- and excited-state absorber populations. Furthermore, such a coupled system cannot be described as a scaled sum of the bare molecular and cavity responses.


Classical Modeling of Transmission through an Absorptive Media
The transmittance spectra were calculated according to the following expression for transmission through a Fabry-Pérot cavity filled with an absorptive media.
In this expression,  is frequency, R mirror reflectivity,  the absorption coefficient, L cavity length, n refractive index, and  the phase shift upon reflection. Both  and n are frequency-dependent and are described by a Lorentzian oscillator model shown as Eq. S2 and S3 with 1 and 2 defined in Eq. S4 and S5.
To account for distinct ground and excited-state populations, 1 and 2 can consist of multiple states corresponding to elements in the series over i. Calculation of transient spectral response can be done by varying the amplitude factors, Ai in 1 and 2 to mimic population changes.
Below, we showed the spectral cut of 2D IR at ω1= ωdark. It shows derivative feature on the UP side and a large absorptive feature on the LP side. Clearly, this cannot be modeled by the filtered approach (blue trace in Figure 2). Thus even the dark mode spectra cut is not due to the spectral filter effect. Figure 1. Spectral cut at ω1= ωdark of Figure 3(b)

Calibration of 2D IR Excitation Intensities
To properly determine any 2D IR contribution from uncoupled molecules but interacted by the filtered IR spectra through polariton samples, it is necessary conduct these measurements and the regular 2D IR on polariton samples under the same laser excitation conditions. We start by deriving how to determine the filtered 2D IR spectra from uncoupled molecules. Assuming there is a 2D IR response from the uncoupled molecules due to interaction with the pump and probe electromagnetic fields, its signal in the time domain should be: which can be simplified to 2 ( ; 2 , 1 ) ∝ { * 1 * 2 * 3 }( ; 2 , 1 ) .

(S7)
This is the convolution of the three pulses with the response function of the system. Because the 2D IR signals are presented in the frequency domain, which involves the Fourier transform of 2 ( ; 2 , 1 ) ( ( 2 ( ; 2 , 1 ))) amplified by the local oscillator, In the derivation above, we applied the convolution theorem and the self-heterodyne local oscillator field, i.e., where the product of E1 and E2 comprise the filtered pump pulse, 1 ( ) * 2 ( ) = , ( ) (S11) and the product of E3 and ELO comprise the filtered probe pulse, Here, { } is the 2D IR spectrum under impulsive limit assumption, and thereby can be represented by the broadband pump probe.
When the system interacts with the filtered pump/probe pulse, it produces the signal Where Ipump/probe,filtered are the intensities of the corresponding lasers, and Ipump/probe are the incoming laser intensities before passing through polaritons. Ipump/probe, filtered=Ipump/probe*F. It is straight forward to rewrite Eq. S13 into ∝ * 2 (S14) Where Smolecule is the 2D IR response of molecular samples when interacting with broadband pulses without polariton filtering, and it can be experimentally measured. Practically, to avoid saturating the detector, the IR probe intensity is attenuated when measuring Smolecule, so that , = * , where An is the attenuation factor. Thus, the 2D IR signal of molecules after attenuating the IR probe beam is Smolecule,an=Smolecule*An, and ∝ , / * 2 (S15) The last step is to determine F, which where Fan is the ratio between the experimentally measured polariton filtered IR probe spectrum and the attenuated full broadband IR spectra. Combining Eqs. S15 and 16, we get = , * 2 * = , * * (S17) Where , and Fan are both experimentally measured and the attenuation factor, An = 0.21 (Fig.S1).
We obtain the experimentally filtered 2DIR by inserting a polariton sample on the probe path to filter the probe beam, and use the pulse shaper to create pump pulses whose spectral lineshape matches the polariton spectrum. Because the shaped pump power and the pump power after the polariton samples are different, we need to scale the experimentally measured filtered spectra by a scale factor SF, in order to obtain the SEf measured under the same condition as the regular 2D IR of polaritons.  Figure S2. The molecular spectra and corresponding pump and probe filters for the filtered spectra. Following Eq.S17, the broadband 2D IR spectrum (Smolecular,an) of the uncoupled molecules are multiplied by the polariton linear transmission spectra along the ω1 (F), and ω3 (Fan) axes, respectively, to generate the filtered spectra (Sf) . The noted signal intensity of Smolecular,an has the same spectral location (1965,2002) of the peak in the filter spectra (noted by *), using Eq.S17, by multiplying the intensity of (1965,2002) of Smolecular,an by F*Fan, the peak intensity at the same position of Sf can be obtained.

Fitting results of the polariton dynamics.
We fitted the LP dynamics using the following kinetic model, and the fitted results are shown in Fig.5.
Because it is known that at long time delay, the LP dynamics reflect the 1-2 transition of the dark reservoir modes, we used the kinetic model below to describe its dynamics.
The result is summarized in Table S1. k 10 become slightly faster under VSC comparing to outside cavity, which remain to be further investigated. The biggest effect is that the relative population between 2 nd and 1 st excited states (P2/P1) change when the thickness are tuned, with the thinner spacers more effectively exciting the 2 nd excited state. This phenomenon could be related to the hot vibrational dynamics reported by some of the authors. Table S1. Fitting results of Figure 5. 6um 12um 25um Outside of cavity P2/P1 18.6 9.7 2.6 0 T 10 = 1/k 10 (ps) 112 130 107 153